This is an interesting argument as we are in completely unknown territory.
As is it now we have some of the oldest scripts still readable because of pure luck (they were trapped in specific materials that preserved them, stayed in unopened cave etc.), extremely high effort (actively kept in pristine condition, backed up, repaired as needed) or wide appeal (e.g. religious books, reference books)
Basically we don't have much of the random papers circulating in markets and left lying around when their appeal was pretty small.
I think the same process will still happen with digital data, there will be a very low chance to find back the integrality of random users facebook posts, or the verge's amazon echo reviews in 4 centuries. But the work of the 'digital monks' will still be a lot easier, and I'd expect the bar to preserve any specific content to be a lot lower than what we had in the past.
Say, people's cooking recipes might survive a few centuries more, and possibly at a massive scale if a few dozens of people take the time to make that happen, where in the past this would just be unrealistic.